For any field \(f(x)\)  the set of all field values greater than or equal to a certain field threshold, \(f=u_{th}\)  is called an excursion set. The boundary curves of these excursion sets in two dimensions enclose either a connected region (regions formed by bounded curves enclosing a set of values greater than or equal to \(u_{th}\) ) or a hole (regions formed by bounded curves enclosing a set of values less than \(u_{th}\) ). The number of connected regions, \(n_{con}\)  and holes, \(n_{hole}\)  at the threshold \(u_{th}\)  are called Betti numbers. Minkowski functionals describe the morphology and topology of excursion set regions for a given random field as a function of field threshold \(u_{th}\) . The morphology and number of these excursion set regions changes as \(u_{th}\)  is varied.
Minkowski Tensors (MTs) are tensor generalization of the Scalar Minkowski Functionals. We will focus on the translation invariant symmetric rank two tensor, which we refer to as the contour MT (CMT), defined for a single boundary curve \(C\)  as [1]}:
\(\mathcal {W}_{1}=\int _C \hat{T}\otimes \hat{T} ~{\rm d}s,\) 
